Recent progress in x-ray optics has pushed the lateral resolution of soft x-ray magnetic microscopy to below 15 nm. We have measured local magnetic hysteresis on a nanometer scale at the full-field x-ray microscope XM-1 at the Advanced Light Source in Berkeley, approaching fundamental length scales such as exchange lengths, Barkhausen lengths, and grain diameters. We have studied the evolution of magnetic domain patterns in a nanogranular CoCrPt film with a pronounced perpendicular magnetic anisotropy and revealed nanoscopic details associated with the granular film structure. From a quantitative analysis of the field-dependent magnetic domain patterns, we are able to generate local magnetic hysteresis map on a nanometer scale. Our findings indicate a significant variation of local coercive fields corresponding to the nanoscopic behavior of magnetic domains. (C) 2006 American Institute of Physics.